About periodic and quasi-periodic orbits of a new type for twist maps of the torus
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| Format: | Artículo científico |
| Langue: | en |
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Academia Brasileira de Ciências
2002
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| _version_ | 1876450265295486976 |
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| author | Salvador Addas Zanata |
| author_facet | Salvador Addas Zanata |
| contents | About periodic and quasi-periodic orbits of a new type for twist maps of the torus Salvador Addas Zanata Multidisciplinaria (Ciencias Naturales y Exactas) Nielsen twist maps Thurston theory topological methods vertical rotation number We prove that for a large and important class of C1 twist maps of the torus periodic and quasiperiodicorbits of a new type exist, provided that there are no rotational invariant circles (R.I.Cs).These orbits have a non-zero vertical rotation number (V.R.N.), in contrast to what happens toBirkhoff periodic orbits and Aubry-Mather sets. The V.R.N. is rational for a periodic orbit andirrational for a quasi-periodic. We also prove that the existence of an orbit with a V.R.N = a > 0,implies the existence of orbits with V.R.N = b, for all 0 < b < a. And as a consequence ofthe previous results we get that a twist map of the torus with no R.I.Cs has positive topologicalentropy, which is a very classical result. In the end of the paper we present some applications andexamples, like the Standard map, such that our results apply. 2002 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32774103 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.1 Vol.74 |
| format | Artículo científico |
| id | redalyc_32774103 |
| institution | Redalyc |
| language | en |
| publishDate | 2002 |
| publisher | Academia Brasileira de Ciências |
| spellingShingle | About periodic and quasi-periodic orbits of a new type for twist maps of the torus Salvador Addas Zanata Multidisciplinaria (Ciencias Naturales y Exactas) Nielsen twist maps Thurston theory topological methods vertical rotation number About periodic and quasi-periodic orbits of a new type for twist maps of the torus Salvador Addas Zanata Multidisciplinaria (Ciencias Naturales y Exactas) Nielsen twist maps Thurston theory topological methods vertical rotation number We prove that for a large and important class of C1 twist maps of the torus periodic and quasiperiodicorbits of a new type exist, provided that there are no rotational invariant circles (R.I.Cs).These orbits have a non-zero vertical rotation number (V.R.N.), in contrast to what happens toBirkhoff periodic orbits and Aubry-Mather sets. The V.R.N. is rational for a periodic orbit andirrational for a quasi-periodic. We also prove that the existence of an orbit with a V.R.N = a > 0,implies the existence of orbits with V.R.N = b, for all 0 < b < a. And as a consequence ofthe previous results we get that a twist map of the torus with no R.I.Cs has positive topologicalentropy, which is a very classical result. In the end of the paper we present some applications andexamples, like the Standard map, such that our results apply. 2002 artículo científico 0001-3765 https://www.redalyc.org/articulo.oa?id=32774103 en http://www.redalyc.org/revista.oa?id=327 Anais da Academia Brasileira de Ciências application/pdf Academia Brasileira de Ciências Anais da Academia Brasileira de Ciências (Brasil) Num.1 Vol.74 |
| title | About periodic and quasi-periodic orbits of a new type for twist maps of the torus |
| topic | Multidisciplinaria (Ciencias Naturales y Exactas) Nielsen twist maps Thurston theory topological methods vertical rotation number |
| url | https://www.redalyc.org/articulo.oa?id=32774103 |